Prediction of low-modulus Ti-based refractory high-entropy alloys for orthopedic implants using machine learning and DFT calculations

Abstract

Designing metallic biomaterials with elastic properties comparable to human bone is a key challenge in orthopedic implant development. This study presents an integrated machine learning (ML) and density functional theory (DFT) framework to accelerate the discovery of biocompatible refractory high-entropy alloys (RHEAs). A dataset comprising eight key descriptors was used to train six ML models, with CatBoost achieving the highest accuracy (R² = 0.99 training, 0.97 testing; RMSE = 0.1 GPa). SHAP analysis identified atomic radius, electronegativity, and valence electron concentration as dominant factors influencing elasticity. The framework was applied to TiZrNbX (X = Ta, Hf, V, Mo, W, Re, Cr) alloys. ML-predicted young's moduli (74.5–172.4 GPa) closely matched DFT results (57.8–156.1 GPa). TiZrNbHf, with its low modulus and favorable ductility, emerged as a promising implant candidate. This work demonstrates the effectiveness of ML-DFT integration for rapid, interpretable, and targeted design of next-generation orthopedic materials.